Pricing of Embedded Inflation Options

This work uses stochastic scenarios to value embedded inflation options in insurance products. These scenarios are generated using the Jarrow Yildirim model. Three processes are modelled: nominal interest rates, real interest rates and an inflation index. The Hull-White model is used in this setting to model the nominal interest rate. Analytical formulas can be derived to price inflation-indexed derivatives. We will examine how these formulas can be used to calibrate the model to match market prices in order to obtain model parameters. We show that the calibration depends heavily on which instruments are used in the calibration. Using these model parameters, stochastic scenarios can be constructed. We demonstrate how embedded inflation options containing a path dependency can be valued using scenarios, and further provide prices of embedded inflation options of a fictional pension contract.